# Pseudo random binary signal system identification of two numbers

Year of fee payment: The present invention discloses a pseudo-random bit sequence PRBS generator which outputs the entire datapath, or entire pseudo-random bit sequence, over one single clock cycle. This is accomplished by removing redundancy, or any redundant exclusive-or gates from linear feedback shift registers; using logic to identify the critical path and optimal shift for the critical path; and dividing the datapath into several pipeline stages to increase the clock rate i.

Claims priority to Canadian Application No. The utility of such random numbers includes the creation of cryptography keys, the generation of bit stream ciphers and hash functions, and the testing of circuits and circuit simulations to detect and correct design errors. An LFSR consists of a series of flip-flops connected by Exclusive-Or XOR gates, allowing for the output of one or more flip-flops to be input into a subsequent flip-flop.

Because LFSRs vary in size 4-bits, bits, bits, etcthey will repeat themselves once each bit location or stage is fed back and input into the first bit location. Therefore, in a four-bit LFSR, for each bit to be output from each bit location requires 4 clock periods, where one bit is output each cycle. The input bit is therefore a result of a linear function of the present state LFSR the XORing of bits from the LFSRwith next state data shifting cyclically through the circuit through a feedback loop to generate a pseudo-random output 2.

The LFSR generates a PRBS pattern, which may appear to be truly random but is actually pseudo random due to the deterministic nature of computer-based operations: In the first clock cycle, the latter two bit locations of the present state, x 3 and x 4are XORed together and fed back into the pseudo random binary signal system identification of two numbers bit location, x 1so the new value x 3 XOR x 4 is located in the first bit location and the x I value is shifted into the second bit location formerly x 2.

As illustrated in FIG. First, there is a large amount of latency produced where the LFSR can only output one bit per clock cycle: The speed of the output also depends on the number of XOR gates the data must travel through; the larger the size of the LFSR, the larger the size of the logic element required to accommodate it, and the larger the number of XOR gates needed.

Typically, an n-bit LFSR has pseudo random binary signal system identification of two numbers data bits in bit locations 1 -n and 1 bit is output from the datapath each clock cycle. Therefore, after n clock cycles or periods, an n-bit PRBS pattern has been output. However, the present invention discloses a method to reduce the latency of PRBS Generation by 1 removing redundancy, or redundant XOR gates; 2 employing foresee logic to identify the critical path and optimal shift for the critical path; and 3 dividing the datapath into several pipeline stages to increase the clock rate, thereby outputting the entire datapath in one clock cycle.

The present invention aims to reduce the latency associated with Pseudo-Random Bit Sequence PRBS Generation by outputting an entire datapath in one clock cycle or period, as opposed to the prior art practice of outputting one single bit in one clock cycle or period. This would imply that for an n-bit LFSR, the datapath would shift n times each clock cycle to output the entire n-bit datapath. However, the present invention employs a combinational logic element to foresee the next state, eliminating any wait time associated with the n-bit datapath shift.

It should be pseudo random binary signal system identification of two numbers that the 4-bit LFSR 11 is illustrated for demonstrative purposes only and should not be considered to limit the scope of the invention, as the invention may be applicable to any size LFSR. The LFSR 11instead of XORing data from the final two bit locations 11 c, 11 d and feeding back the new value to the first bit location 11 aas shown in the prior art example of FIG.

Note that this combinational logic 13 has no register and therefore is not controlled by a clock. The next state as determined by combinational logic 13 is then fed back to LFSR 11 as the new present state. The ability of the combinational logic 13 to foresee or calculate the next state and feed the value back to the original LFSR 11 as the new present state eliminates the need to output all n-bits from the datapath by shifting all n-bits in the LFSR 11which is critical in reducing the PRBS Generation latency.

In addition to providing the ability to foresee the next state, the combinational logic element also provides the ability to identify the critical path. The critical path is important as it acts as the signal which determines the overall frequency of the PRBS Generator. After the seventh shift 3 g we see a total of 4 XOR gates in the first bit location, but the redundant even-numbered values cancel each other out to leave only 2 XOR gates remaining in the first bit location.

Therefore, the smallest and most efficient shift for the critical path is 3. This number is identified through the use of software or another hardware platform which removes redundancy by removing all even-numbered Pseudo random binary signal system identification of two numbers gates and removing all but one odd-numbered XOR gates, and subsequently identifies the critical path, as, again, the maximum number of XOR gates between registers.

The software or other hardware platform then iterates through all possible bit shifts to determine the optimal bit-shift for the critical path.

The size of the combinational logic 13 used to determine the next state is directly correlated to the size of the LFSR and therefore the size of the datapath.

For example, a 4-bit LFSR will necessitate a 4-bit combinational logic element, a bit LFSR will necessitate a bit combinational logic element; a bit LFSR will necessitate a bit combinational logic element, etc. Therefore, both the combinational logic and the critical path may be too large. To reduce the size and latency of the PRBS Generator, the datapath may be reduced by splitting it into several pieces, or pipeline stages.

The pipeline consists of multiple blocks connected as a series, where the data output from one pipeline stage is input **pseudo random binary signal system identification of two numbers** a next pipeline stage. When two or more LFSRs are arranged in pipeline stages band each clock cycle or **pseudo random binary signal system identification of two numbers** outputs a number of bits from each pipeline stage b which are then concatenated as the total output, the latency of the PRBS Generator is reduced.

In an illustrative embodiment of the present invention, PRBS Generation occurs over a bit OTU 3 datapath, where software or another hardware platform is used to remove redundancy by removing all even-numbered XOR gates and removing all but one odd-numbered XOR gates, subsequently identifying the critical path, and the software or other hardware platform then iterates through all possible bit-shifts to identify the optimal shift for the critical path.

For a bit OTU 3 datapath, the critical path is 32 bits as described above. The contents of each pipeline stage are expanded in FIG. As shown in FIG. From register 21 1 the data is fed into the next pipeline stage 14 2 where the data in register 21 2 is similarly pseudo random binary signal system identification of two numbers. This process is repeated until the value reaches the final register 21 bwhereby the value, or the next state, is fed back to the first register 17 as the new present state.

As in initialization phase, from register 21 1 the data is fed into the next pipeline stage 14 2 where the data in register 21 2 is similarly shifted.

The process is repeated until the value reaches the final register 21 band the value, or the next state, is again fed back to the first register 17 as the new present state. In this illustrative embodiment of the present invention, each pipeline stage b register 21 1 - b represents the logic shifted by the previous stages, so the first register 21 1 outputs data into a second register 21 2 and shifts the data in the second register 21 2 by 32 bits; the second register 21 2 outputs data into a third register 21 3 not shown and shifts the data in the third register 21 3 by 32 bits; this continues until the second-to-last register 21 b - 1 outputs data into a final register 21 b and shifts the data in the final register 21 b by 32 bits.

In the illustrative pseudo random binary signal system identification of two numbers of the present invention, the data shift output over each clock cycle equals 32 bits per pipeline stage, with 8 pipeline stages, which when concatenated produces the first full bit datapath.

The flexibility of up to options allows for the most optimal path to be chosen. A number of equations to identify the critical path can be determined. In normal mode, x bits are output from each register at every clock cycle: A pseudo-random bit sequence generator, comprising: The pseudo-random bit sequence generator of claim 1wherein said independent datapath stages are pipeline stages.

The pseudo-random bit sequence generator of claim 1 pseudo random binary signal system identification of two numbers, wherein said datapath is output once per clock cycle, whereby said pseudo-random bit sequence is output once per clock cycle.

The pseudo-random bit sequence generator of claim 1wherein said deterministic logic element is a software element. The pseudo-random bit sequence generator of claim 1wherein said deterministic logic element is a hardware platform. CA CAA1 en US USB2 en System and method for producing functions for generating pseudo-random bit sequences.

System and method for determining the Nth state of linear feedback shift registers. Bit error rate tester using fast parallel generation of linear recurring sequences.

Method and apparatus for generating a random number using the meta-stable behavior of latches. High quality uniform random number generation using LUT optimised state-transition matrices. Test pattern generation circuit having plural pseudo random number generation circuits supplied with clock signals at different timing respectively. Digital signal processing circuit selectively operable in either a normal or a pseudorandom noise generative mode.

M Year of fee payment:

Lingua di insegnamento Inglese. The course aims to introduce the main techniques for identifying discrete time systems with particular reference to the family of equation errors models used for prediction and control.

The main arguments that pseudo random binary signal system identification of two numbers presented in the course are stochastic optimal estimation, Kalman prediction and filtering in the discrete time setting and advanced digital control schemes.

At the end of the course students are able to run basic identification algorithms for linear systems and to master design and implementation aspects of digital control systems. Introduction Systems and models. Classification of models by modeling objectives. Physical modeling and system identification. Brief review of stochastic processes Random stochastic processes. First and second order moments: Stationary and weakly stationary processes. Sample estimates of first and second order moments.

Cross-correlation and cross-covariance of two stochastic processes. Independence, uncorrelatedness and orthogonality. Vector stochastic processes and their first and second order moments. Stochastic models Modeling disturbances by filtering white noise: System representation by means of backward and forward shift operators. FIR models as approximations of impulse responses. Output error models and Box-Jenkins models.

The identification problem Definition of the identification problem. Parameter estimation and model order estimation. Identifiability and the concept of the true model. Covariance of the estimate and its use as performance index. The least squares Introduction to the least squares LS method: Derivation of the LS estimate. Geometrical interpretation of the LS estimate. Derivation of the LS estimate in the geometrical framework: Statistical properties **pseudo random binary signal system identification of two numbers** the LS estimator in the static case.

The best linear unbiased estimator. Least squares identification of dynamic equation error models. LS identification pseudo random binary signal system identification of two numbers FIR models and its statistical properties.

LS identification of ARX models. Consistency of the estimate. LS identification of autoregressive models. Identifiability properties of LS estimates: Persistency of excitation of input signals.

PE properties of some possible input signals: Recursive least squares RLS identification. Choice of the initial values.

Recursive weighted least squares. Choice of the forgetting factor. Asymptotic behavior of RLS algorithms. Model order estimation and model validation The chi-square distribution and its properties. Errors of type I and II. Example of statistical hypothesis test. Asymptotic properties of the residual of the least squares estimation.

Model order estimation methods: F-test, final prediction error criterion. Criteria with complexity terms: Akaike information criterion, minimum description length criterion. The prediction error method. Introduction to the Newton-Raphson algorithm. Evaluation of the gradient of the residual. Choice of the initial estimate. Statistical properties of the PEM estimator. The instrumental variable method Introduction to the instrumental variable IV method.

Statistical properties of the IV estimator. Brief notes on extended IV methods. Identification of MA models.

Approximation of MA models with high-order AR models. Maximum likelihood Introduction to maximum likelihood estimation. Covariance of the estimate: The fundamental theorem of estimation theory: Properties of the optimal linear estimator. Optimal estimation of signals: Brief recalls on the Luenberger observer. Stochastic state space models.

Derivation of the Kalman filter equations by means of the properties of the optimal linear estimator. The Kalman predictor and the difference Riccati equation.

Convergence of the difference Riccati equation. The steady-state suboptimal Kalman predictor. Some extension of the standard Kalman filter: Dealing with colored noises: Guidorzi, Multivariable System Identification: From Observations to Models. Bononia University Press, Bologna, Theory for the User. Prentice Hall, Englewood Cliffs, N. Bittanti, "Identificazione dei modelli e sistemi adattativi", Pitagora Editrice Bologna, in italian. Bittanti, "Teoria della predizione e del filtraggio", Pitagora Editrice Bologna, in italian.

Consulta il sito web di Roberto Diversi. Pseudo random binary signal system identification of two numbers mia e-mail Studenti La mia e-mail Personale Chiudi. Home Futuri studenti Studenti iscritti Studenti internazionali Laureati. Metodi didattici Traditional lectures. Strumenti a supporto della didattica Video projector, blackboard Link ad altre eventuali informazioni http:

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